Can a set of 6 sided die, simulate any other die?

Question

So suppose I only have 6 sided dice, or D6. I want to play an RPG where a D20, or D10 is required. Can I simulate a D20 or D10 or any other sided die, using one or more D6?

Answer 1

If you’re willing to roll the dice as often as necessary to get a result, you can use a D$6$ (or any other die you’d like) to emulate any die you’d like. Just think of a roll of the die (minus $1$) as the next digit in a fraction written in base $6$. There is a probability of $1$ that you’ll get a determinate result after finitely many rolls.

Answer 2

To complete the answer, there is no way to use D$6$ to emulate D$10$ with a guaranteed finite number of rolls. Suppose you roll $N$ times. There are $6^N$ possible results. However, since $6^N$ is not a multiple of $10$, you cannot divide the results into $10$ equal subsets.